LETTER Communicated by Benjamin Schrauwen Regularized Variational Bayesian Learning of Echo State Networks with Delay&Sum Readout

In this work, a variational Bayesian framework for efficient training of echo state networks (ESNs) with automatic regularization and delay&sum (D&S) readout adaptation is proposed. The algorithm uses a classical batch learning of ESNs. By treating the network echo states as fixed basis functions parameterized with delay parameters, we propose a variational Bayesian ESN training scheme. The variational approach allows for a seamless combination of sparse Bayesian learning ideas and a variational Bayesian space-alternating generalized expectationmaximization (VB-SAGE) algorithm for estimating parameters of superimposed signals. While the former method realizes automatic regularization of ESNs, which also determines which echo states and input signals are relevant for "explaining" the desired signal, the latter method provides a basis for joint estimation of D&S readout parameters. The proposed training algorithm can naturally be extended to ESNs with fixed filter neurons. It also generalizes the recently proposed expectationmaximization-based D&S readout adaptation method. The proposed algorithm was tested on synthetic data prediction tasks as well as on dynamic handwritten character recognition. Neural Computation 24, 967-995 (2012

Training Echo State Networks with Regularization through Dimensionality Reduction

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network

Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.Comment: 41 page

Analog readout for optical reservoir computers

Reservoir computing is a new, powerful and flexible machine learning technique that is easily implemented in hardware. Recently, by using a time-multiplexed architecture, hardware reservoir computers have reached performance comparable to digital implementations. Operating speeds allowing for real time information operation have been reached using optoelectronic systems. At present the main performance bottleneck is the readout layer which uses slow, digital postprocessing. We have designed an analog readout suitable for time-multiplexed optoelectronic reservoir computers, capable of working in real time. The readout has been built and tested experimentally on a standard benchmark task. Its performance is better than non-reservoir methods, with ample room for further improvement. The present work thereby overcomes one of the major limitations for the future development of hardware reservoir computers.Comment: to appear in NIPS 201

Transient Information Flow in a Network of Excitatory and Inhibitory Model Neurons: Role of Noise and Signal Autocorrelation

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation on the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.Comment: 27 pages, 7 figures, to appear in J. Physiology (Paris) Vol. 9

Neuroevolution on the Edge of Chaos

Echo state networks represent a special type of recurrent neural networks. Recent papers stated that the echo state networks maximize their computational performance on the transition between order and chaos, the so-called edge of chaos. This work confirms this statement in a comprehensive set of experiments. Furthermore, the echo state networks are compared to networks evolved via neuroevolution. The evolved networks outperform the echo state networks, however, the evolution consumes significant computational resources. It is demonstrated that echo state networks with local connections combine the best of both worlds, the simplicity of random echo state networks and the performance of evolved networks. Finally, it is shown that evolution tends to stay close to the ordered side of the edge of chaos.Comment: To appear in Proceedings of the Genetic and Evolutionary Computation Conference 2017 (GECCO '17

Hierarchical Temporal Representation in Linear Reservoir Computing

Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical temporal representation in deep RNNs through frequency analysis applied to the state signals. The potentiality of our approach is assessed on the class of Multiple Superimposed Oscillator tasks. Furthermore, our investigation provides useful insights to open a discussion on the main aspects that characterize the deep learning framework in the temporal domain.Comment: This is a pre-print of the paper submitted to the 27th Italian Workshop on Neural Networks, WIRN 201